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Time-to-depth conversion and seismic velocity estimation using time-migration velocity

Maria Cameron, Sergey Fomel and James Sethian
Time-to-depth conversion and seismic velocity estimation using time-migration velocity (in Velocity estimation for depth imaging, William S. Harlan (editor), Robert T. Langan (editor) and Tamas Nemeth (editor))
Geophysics (September 2008) 73 (5, Suppl.): VE205-VE210

Abstract

The objective was to build an efficient algorithm (1) to estimate seismic velocity from time-migration velocity, and (2) to convert time-migrated images to depth. We established theoretical relations between the time-migration velocity and seismic velocity in two and three dimensions using paraxial ray-tracing theory. The relation in two dimensions implies that the conventional Dix velocity is the ratio of the interval seismic velocity and the geometric spreading of image rays. We formulated an inverse problem of finding seismic velocity from the Dix velocity and developed a numerical procedure for solving it. The procedure consists of two steps: (1) computation of the geometric spreading of image rays and the true seismic velocity in time-domain coordinates from the Dix velocity; (2) conversion of the true seismic velocity from the time domain to the depth domain and computation of the transition matrices from time-domain coordinates to depth. For step 1, we derived a partial differential equation (PDE) in two and three dimensions relating the Dix velocity and the geometric spreading of image rays to be found. This is a nonlinear elliptic PDE. The physical setting allows us to pose a Cauchy problem for it. This problem is ill posed, but we can solve it numerically in two ways on the required interval of time, if it is sufficiently short. One way is a finite-difference scheme inspired by the Lax-Friedrichs method. The second way is a spectral Chebyshev method. For step 2, we developed an efficient Dijkstra-like solver motivated by Sethian's fast marching method. We tested numerical procedures on a synthetic data example and applied them to a field data example. We demonstrated that the algorithms produce a significantly more accurate estimate of seismic velocity than the conventional Dix inversion. This velocity estimate can be used as a reasonable first guess in building velocity models for depth imaging.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 73
Serial Issue: 5, Suppl.
Title: Time-to-depth conversion and seismic velocity estimation using time-migration velocity
Title: Velocity estimation for depth imaging
Author(s): Cameron, MariaFomel, SergeySethian, James
Author(s): Harlan, William S.editor
Author(s): Langan, Robert T.editor
Author(s): Nemeth, Tamaseditor
Affiliation: New York University, Department of Mathematics, New York, NY, United States
Affiliation: Landmark Graphics, Highlands Ranch, CO, United States
Pages: VE205-VE210
Published: 200809
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 18
Accession Number: 2009-085042
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus.
Secondary Affiliation: Chevron, USA, United StatesUniversity of Texas at Austin, USA, United StatesUniversity of California at Berkeley, USA, United States
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2018, American Geosciences Institute. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 200946
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